Suppose the marginal product of labor is MPN = 200 - 0.5N where N is aggregate employment. The aggregate quantity of labor supplied is 300 + 8w, where w is the real wage. What is the equilibrium quantity of employment?

Equillibrum quantity of employment = 380

Explanation:

At equillibrum real wage (w) is equal to marginal product of labour (MPN)

MPN = 200-0.5N

Aggregate supply = 300+8w

At equilibrium w = MPN

At equillibrum Aggregate demand (N) = Aggregate Supply

w = 200-0.5N

w = 200-0.5 (300+8w)

w = 200-150-4w

4w+w = 50

5w = 50

w = 10

Substitute value of w in w = 200-0.5N

10 = 200-0.5N

0.5N = 200-10

0.5N = 190

N = 190/0.5 = 380

10

Explanation:

The margin product of labor (MPN) = 200 - 0.5N

Aggregate quantity of labor supplied, N = 300 + 8w

Note: In labor market equilibrium, marginal product of labor is equivalent to real wage (w),

Thus real wage (w) can be calculated as:

w = 200 - 0.5N

w = 200 - 0.5 (300+8w)

w = 200 - 150-4w

Collecting of like terms:

w + 4w = 200 - 150

5w = 50

w = 50/5

w = 10

Thus, the required equilibrium real wage (w) in the market = 10